On the probabilistic complexity of numerically checking the binary Goldbachconjecture in certain intervals

A heuristic analysis is presented of the complexity of an algorithm which was applied recently to verify the binary Goldbach conjecture for every integer in the interval $[4,10^{14]$, as well as for every integer in $[10^k,10^k+10^9]$, for different values of $k$ up to 300. The analysis agrees reasonably well with the experimental observations